Least Common Multiple (LCM) of 123 and 81
The least common multiple (LCM) of 123 and 81 is 3321.
What is the Least Common Multiple (LCM)?
The LCM of two integers is the smallest positive integer that is divisible by both numbers. It is often used to find common denominators and solve problems involving periodic events.
Formula for LCM
The LCM of two numbers can be calculated using their GCD:
LCM(a, b) = |a × b| ÷ GCD(a, b)
How to Calculate the LCM of 123 and 81?
First, calculate the GCD of 123 and 81 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 123 ÷ 81 = 1 remainder 42 |
| 2 | 81 ÷ 42 = 1 remainder 39 |
| 3 | 42 ÷ 39 = 1 remainder 3 |
| 4 | 39 ÷ 3 = 13 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 105 and 71 | 7455 |
| 160 and 82 | 6560 |
| 78 and 37 | 2886 |
| 76 and 102 | 3876 |
| 103 and 193 | 19879 |